where η ∈ 0, 1 , α, β ∈ R, f ∈ C 0, 1 × R,R . The parameters α and β are arbitrary in R such that 1 2α 2βη − 2β / 0. Our aim is to give new conditions on the nonlinearity of f , then using Leray-Schauder nonlinear alternative, we establish the existence of nontrivial solution. We only assume that f t, 0 / 0 and a generalized polynomial growth condition, that is, there exist two nonnegative func...

Let μ be a nonnegative Radon measure on R which only satisfies the following growth condition that there exists a positive constant C such that μ B x, r ≤ Cr for all x ∈ R, r > 0 and some fixed n ∈ 0, d . In this paper, the authors prove that for suitable indexes ρ and λ, the parametrized g∗ λ function M∗,ρ λ is bounded on L μ for p ∈ 2,∞ with the assumption that the kernel of the operator M∗,ρ...

We present a Zariski pair in affine complex plane consisting of two line arrangements, each of which has six lines. In the seminal paper [3], Zariski started the study of the fundamental groups of the complements of plane algebraic curves. Among other things, he constructed a pair of plane curves with the same degree and the same local singularities, but non-isomorphic fundamental groups, which...

and Applied Analysis 3 refer the reader to 11–13 . In order to represent the mild solutions via the variation of constants formula for this case, the notion of so-called resolvent for the corresponding linear equation x′ t A [ x t ∫ t 0 F t − s x s ds ] , t ∈ J 1.8 can be applied. More precisely, an operator-valued function R · : J → L X is called the resolvent of 7 if it satisfies the followin...

In this study, we construct the difference sequence spaces lp (P?2q) = (lp)P?2q, 1 ? p ?, where P (?rs) is an infinite matrix of Padovan numbers %s defined by ?rs {?s/?r+5-2 0 s r, > r. and ?2q a q-difference operator second order. We obtain some inclusion relations, topological properties, Schauder basis ?-, ?- ?-duals newly space. characterize certain classes from space to any one l1, c0, ...

This study investigates the effect of orthographic forms on phonetic aspects isolated speech sound production and perception. Three groups 25 L1-Spanish speakers were exposed to /y/ /?/ in a multi-session learning study. They heard same vowels presented with: L1-incongruent forms, novel or without forms. After three exposure sessions, participants tested vowel an elicited task perception multip...

Fair cake-cutting is the division of a cake or resource among N users so that each user is content. Users may value a given piece of cake differently, and information about how a user values different parts of the cake can only be obtained by requesting users to “cut” pieces of the cake into specified ratios. Many distributed computing problems which involve resource sharing can be expressed as...

A combined computational and experimental study of the coordination chemistry of phosphine-alkene ligand L1 (N-diphenylphosphino-7-aza-benzobicyclo[2.2.1]hept-2-ene) with Pd(0) and Pd(II) is presented. Experimentally it is established that ligand L1 promotes direct alkyl-alkyl and indirect alkyl-halide reductive elimination from Pd(II) species, affording the palladium(0) complex [Pd(κ(2)-P,C-L1...